Let the smallest positive value of for which the function

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Let the smallest positive value of

x

for which the function

f(x)=\sin\left(\frac{x}{3}\right)+\sin\left(\frac{x}{11}\right)

, where

x\in\mathbb{R}

, achieves its maximum value be

x_0

. Express

x_0

in degrees, i.e.

x_0=\alpha^\circ

. Then, the sum of the digits in

\alpha

is (1) 15 (2) 17 (3) 16 (4) 18